Experimental study and numerical analysis of fluid-structure coupling vibration characteristics for the reciprocating compressor pipeline

The fluid-structure coupling has been one of the hot issues of academic research in recent years, the achievements in various fields of study also emerge in an endless stream, but on the current research status, The study of fluid structure interaction in the field of dynamic equipment, especially compressor, is not very common. With the development of industrial compressors in the direction of large-scale and high-parameters, the analysis of coupling characteristics represented by fluid-solid coupling can evaluate the safe and stable operation of the system, and the evaluations are ofen more close to the actual situation. Therefore, it has gradually been valued. Through the comparison and analysis of the vibration test system of the reciprocating compressor before and after the pipeline inflation, the vibration response caused by the coupling factor is obtained, for the correctness verification of the fluid-structure coupling simulation. the numerical model of the experimental system is established based on ANSYS WORKBENCH, and the boundary conditions of the model are simulated by the experimental data, verified the feasibility of simulation program. Finally, the effects of medium density, pressure, flow rate, elastic modulus of pipe and Poisson’s ratio on fluid solid coupling vibration are discussed by using the verified simulation model. The results show that the medium density, dynamic fluid flow rate and pipe Poisson’s ratio have relatively little influence on the fluid-solid coupling vibration of the pipeline, while the medium pressure and the elastic modulus of the pipe have a great influence.


Introduction
The vibration phenomenon of reciprocating compressor pipeline system in practical engineering application is generally the result of multi physical field coupling. The pipeline system is composed of the elastic gas column in the pipeline and the mechanical structure surrounding the gas column fluid. The periodic pressure pulsation of the fluid in the pipe will cause the mechanical vibration of the pipeline. At the same time, the mechanical vibration will change the flow state of the fluid in turn, which is the fluid structure coupling vibration.
In the 1950s and 1960s, Skalak solved infinite wave modes of the pipeline system considering the moment of inertia and bending stiffness of the pipeline, which laid a foundation for the coupling theory of the liquid-filled pipeline; Walker and Phillips [1] considered the effects of Poisson coupling and connection coupling effects as well as the additional mass and the radial inertia of the tube wall, studied the law of short-wavelength fluid pressure pulsation in a straight tube with low elastic modulus, and deduced the equation of vibration; Wiggert and Hatfield [2] proposed a fourteen-equation model describing the vibration of flow-filled pipelines in the study of fluid-structure coupling problems, and the component synthesis method was used for frequency response analysis; Tentarelli [3] first measured the Poisson coupling vibration through experimental method , and explained the effect of Poisson coupling on the dynamic characteristics of pipeline system; Tijsseling and Vardy [4][5] studied the coupling vibration of branch pipes, valves and 90 o curved pipes; S.Ziada [6] et al. Carried out experimental comparative research on the fluid-structure interaction theory of T-shaped pipelines; Duan [7] et al. Studied the Y-shaped pipe and obtained the gas-solid two-phase flow law of the pipe.
Wang Jian [8] et al. Used ALE method to simulate the fluid structure coupling of pipelines, and analyzed the influence of nonlinear dynamic characteristics; Li Haifeng [9] and others, based on ANSYS parametric design language, provided a new way to solve the problem of fluid structure coupling; Ji Hejiong [10] et al. analyzed the natural frequency and vibration mode of the pipeline under two states of empty pipe and liquid-filled pipe through experiments; Zhang Jie [11] et al. used ADINA to analyze the influence of wall thickness on the natural frequency and vibration mode of current-carrying pipelines, and simulated the dynamic response of pipelines when they were filled with liquid; Tao Donglai [12] et al. Conducted a two-way fluid solid coupling numerical simulation study on the lubricating oil pipeline system of the compressor; Zhao Jie [13] et al. analyzed and calculated the coupled vibration characteristics of the empty tube and the gas-carrying tube based on the gas-solid coupling theory and the Galerkin method that suitable for solving the coupled equations; Bai Changqing [14] et al. Used the transient time history analysis method to simulate the dynamic response of the compressor vent pipe under the impact air flow,which based on the three-dimensional dynamic finite element model of fluid structure coupling.
In recent years, the problem of pipeline vibration of reciprocating compressors has increasingly attracted the attention of industry engineers. However, most of the current research on pipeline vibration ignores the effect of gas columns on the pipeline. Although fluid structure coupling is one of the hot topics in current research , But its research in the field of dynamic equipment, especially compressors is not very common, With the development of industrial compressors towards large-scale and high parameters, the analysis of coupling characteristics represented by fluid structure coupling can evaluate the safe and stable operation of the system closer to the actual situation, so it has gradually been paid attention by the industry. At present, most of the research on this problem is focused on the coupling characteristics of different pipe shapes with different methods and software, the research on the influence of some basic parameters such as medium density, flow velocity, pressure, material elastic modulus, Poisson's ratio on fluid-structure coupling characteristics needs to be strengthened. the study of fluid-structure interaction vibration is to more comprehensively analyze the interaction between pipeline structure and fluid flow, and to explore the negligible conditions of fluid-structure interaction. Its research will provide guidance for the solution of reciprocating compressor pipeline vibration problems, and at the same time, it also has important reference value and reference significance for vibration problems in other similar fields.

Experimental Study
In order to explore the law of fluid solid coupling vibration and the specific effect of pressure on it, the experimental study of fluid solid coupling vibration is carried out using the experimental platform shown in Figure 1. In the figure, pipeline 1 and pipeline 2 are experimental pipelines. Six test points are distributed at the connection flanges and elbows of the two pipelines. The red arrows in the figure indicate the airflow direction when the pipelines are circulating. The experimental process is as follows:  Fig.1 Fluid-structure interaction experimental platform First, adjust the relevant valves of the experimental system to make the compressed air flow in the pipeline 1, that is, the pipeline 2 is an empty pipe and the pipeline 1 is an inflation pipe. When the outlet pressure of the first stage compressor is stable at 0.7MPa, use the portable vibration meter to measure the vibration displacement, speed and acceleration of 6 measuring points in the east-west, north-south, up-down directions respectively, and save the experimental data; After completing the above experiments, shut down and adjust the closed state of the valve to allow compressed air to circulate through pipeline 2, that is, at this time, pipe 1 is an empty pipe, and pipe 2 is an inflation pipe. Follow the same steps to complete the subsequent experimental process. After the above experiments, the vibration response data of each measurement point under two experimental conditions can be obtained, as shown in Figures 2 and 3:  From the vibration response curves and analysis of the corresponding vibration data under the two experiments, it can be seen that when the pipeline 1 is inflated, except for the small vibration response at the test point 4, the other three test points have more severe vibrations, especially the three directions of measuring point 2 exceed the vibration standard. In addition, the vibration of the measuring points 5 and 6 on the pipeline 2 is also more severe, after the pipeline 2 was inflated, the vibration displacement of these two measuring points still increased significantly. Among them, the maximum vibration displacement of measuring point 5 increased by 41%, and the maximum displacement rise of measuring point 6 reached 68%. At the same time, under this condition, the maximum vibration displacement of the empty pipeline 1 was reduced by 11%, but at the measuring point 4 where the vibration was originally small, the vibration displacement increased by 46%. In order to explain the change more intuitively, the vibration displacement response of each measuring point under the empty tube and the inflated tube can be obtained by changing the data under the two experiments of measuring points 5 and 6, as shown in Figure 4: It can be seen from Figure 4 that the vibration displacement of the pipeline changes significantly before and after inflation, which indicates that the fluid-solid coupling effect does have a direct impact on the pipeline vibration. Further analysis found that different pipelines have different effects on the fluid-solid coupling effect. Pipeline 2, that is, the branch pipeline of the main pipeline, is also a pipeline with a small overall stiffness, which has a more significant impact, and it shows that fluid-solid coupling will significantly aggravate its pipeline vibration; Pipeline 2, that is, the main pipe connected to the buffer tank at both ends is less affected by fluid-structure interaction. The vibration response at the point of larger vibration will be slightly intensified, while the vibration at the point of smaller vibration will decrease, that is, the curve fluctuation of vibration response has increased.
In order to continue to study the effect of pressure on fluid-structure interaction, two groups of experiments were carried out under the pressure of 0.5MPa and 0.3MPa respectively. From the experimental results of each group, it can be found that pressure does have an effect on fluid-structure interaction, and it affects different pipelines differently, In order to reveal this law, after arranging the experimental data under several pressure conditions, the vibration displacement response of the empty tube and the inflatable tube under each pressure condition can be obtained, as shown in Figure 5 and  It can be seen from Fig.5 that even if the main pipe is in an empty pipe state, the vibration displacement also increases with the increase of pressure, while the branch pipe has the largest vibration when the pressure is the smallest, but it is not a complete inverse correlation, there are no obvious rules to follow. From Figure 6, it can be found that, whether it is the main pipe or the branch pipe, in the state of inflation, the vibration displacement increases with the increase of pressure, and the trend is more obvious in the branch pipe, and the displacement changes more obvious when the pressure is greater. Further analysis of the experimental data shows that the effect of fluid solid coupling is also intensified with the increase of pressure, and the branch pipe with less rigidity is more affected by the fluid solid coupling, for general pipeline vibration analysis, if the internal pressure of the pipeline is less than 0.5MPa, the effect of fluid structure coupling can be ignored. When the pressure is greater than 0.5MPa, the fluid structure coupling effect needs to be considered, especially for some branch pipelines and pipelines with small rigidity.

Numerical simulation
Due to the influence of specific experimental system, the experimental research has great limitations, and can only carry out experiments under specific conditions. If the finite element analysis software is used and the proven coupling field analysis method is adopted, the fluid structure coupling simulation of pipelines under various harsh conditions can be realized, in order to better verify the reliability of numerical simulation, an experimental pipeline is specially selected for numerical modeling and analysis under ANSYS Workbench + CFX software. The actual pipeline is shown in Figure 7.  Fig.7 Actual pipeline diagram Establish two-way fluid-solid coupling analysis options, set the solid domain material density to 7820kg/m 3 , elastic modulus 2.06 × 10 11 Pa, Poisson's ratio 0.3, and the fluid domain will be defined separately in CFX. Given that the model is relatively simple, directly use the software module to model and mesh. Figure 8 shows the meshed solid-domain finite element model.  Figure 9, the outlet boundary condition is set as 0.68MPa, which is slightly less than the pressure after pressure stabilization. The coupling surface is set as wall boundary without sliding. Each coupling surface needs to be consistent with the definition sequence of the fluid part, otherwise the correct coupling surface data may not be ensured during calculation. After the coupling is completed, the fluid will obtain displacement from the solid part, the solid will be forced by the fluid, and the moving grid will cause data transmission on the coupling surface. Fig.9 Pressure boundary conditions at the inlet After the solution control and output control are set, the calculation is performed. After the solution is converged, the total displacement cloud diagram at each calculation time is observed and the maximum grid displacement is 437um, which is consistent with the experimental data in the order of magnitude and the value difference is about 8%. Therefore, it is considered that the numerical simulation results and methods are feasible.  Fig.10 Cloud diagram of total displacement distribution For the effects of media parameters and material parameters that are difficult to study through experiments on pipeline vibration, a validated simulation model can be used for further numerical simulation research to evaluate the reasonable working conditions and material selection from the perspective of vibration reduction. In the following, the above-mentioned simulation examples are used to study the effects of medium pressure, density, flow velocity, material elastic modulus, and Poisson's ratio on fluid-structure interaction vibration of the pipeline by resetting specific parameters.

Medium pressure
In the previous part of this paper, several groups of fluid structure coupling problems under different pressures have been experimentally studied, and the fluid structure coupling vibration of pipeline under 0.7MPa pressure has been numerically simulated. In this section, the numerical simulation of pipeline vibration under 0.6MPa, 0.5MPa, 0.4MPa and 0.3MPa pressure has been continued. The simulation process is similar to that under 0.7MPa, The main change is that the pressure boundary conditions at the inlet and outlet are reset. The simulated displacement cloud diagram of the coupling surface under 0.3 MPa pressure is shown in Figure 11. and the maximum displacement of the grid under different pressure simulations are shown in Table 1:  It can be seen from the above-mentioned displacement distribution cloud diagram and data that the pressure has a significant effect on the vibration of the coupling surface of the pipeline, and the vibration displacement increases with the increase of the pressure. further modal analysis revealed that the corresponding natural frequency of each order also increased with increasing pressure, but this change trend was not as obvious as that of displacement. When the numerical simulation pressure increased geometrically, this trend could be clearly observed, which shows that the influence of pressure pretensioning on the natural frequency of pipeline structure must be considered under high pressure.

Medium density
The initial simulation example in this section of the numerical simulation is air at 25°C and the density is 1.185 kg/m 3 . Considering the actual density of the gas medium and convenient comparison, the research density in this section is 0.185 kg/m 3 , 2.185 kg/m3, 3.185kg/m 3 and 4.185kg/m 3 , other parameters and settings during numerical simulation are consistent with the simulation in the initial calculation. Figure 12 is a cloud diagram of the displacement distribution at a density of 0.185 kg/m 3 . The maximum grid displacement under different density simulations are shown in Table 2:  From the above simulation results, it can be seen that the medium density has little effect on the vibration of the coupling surface of the pipeline, but it also shows a trend of decreasing with the increase of the density. modal analysis found that the natural frequency of each order varies little with the density of the medium in the tube, and the effect is still small when the simulated density changes ten times, especially the first and second order natural frequency change curve is almost straight, which shows that the influence of the medium density on the low order natural frequency is smaller. the above analysis results show that the density of the fluid has a limited effect on the natural frequency of the pipeline and has no effect on the vibration mode shape.

Medium flow rate
In the initial example, the simulated medium flow velocity is 0. For the sake of comparison, this section studies the pipeline vibration under the conditions of 1m/s, 10m/s, 100m/s, and 1000m/s. Other parameters and settings in the numerical simulation are consistent with those in the initial calculation example. Fig.13 is a simulated displacement cloud diagram at a flow velocity of 1 m/s. The maximum grid displacements at each flow rate simulation are shown in Table 3:  Fig.13 The displacement distribution nephogram under 1m/s flow rate  Table 3, it can be seen that the results of the displacement distribution cloud diagrams at other flow rates are not much different from those shown in Figure 13. At the same time, it is noted that the above results have a large increase compared with the case where the flow rate is 0, which indicates that the dynamic fluid affects the pipe vibration It is larger than the static fluid, but the dynamic fluid flow rate has a small impact on pipeline vibration unilaterally. Modal analysis shows that the natural frequency of each order of the pipeline does not change significantly with the velocity of the medium. The overall trend is that the natural frequency increases slightly with the increase of the velocity, but the amplitude is not large. Even when the velocity of the medium increases to 1000 m/s, The maximum frequency variation range is also within 4%, but it is almost impossible to achieve such a high flow rate in an actual pipeline, so the effect of the medium flow rate on the natural frequency of the pipeline can be ignored.

Material elastic modulus
The steel used in the experimental piping system is 20 # carbon steel with an elastic modulus of 2.06 × 10 11 Pa. The numerical simulation in this case has been performed in the initial calculation example. Considering the general range of the elastic modulus of carbon steel and the convenience of numerical comparison, The elastic modulus of the pipeline material in this numerical simulation is specially taken as 1.86 × 10 11 Pa, 1.96 × 10 11 Pa, 2.16 × 10 11 Pa, 2.26 × 10 11 Pa. The simulated displacement distribution cloud diagram with the elastic modulus of 1.86 × 10 11 Pa is shown in Figure 14. The maximum grid displacements under the elastic modulus simulation of each material are shown in Table 4:   It can be seen from the analysis of the results under the above charts that the elastic modulus of the material has a great influence on the vibration of the pipeline, and the smaller the elastic modulus is, the stronger the vibration of the pipeline is. The modal analysis shows that the natural frequency and the modulus of elasticity have obvious positive correlation, and the change ratio of each natural frequency is basically the same under the same modulus of elasticity, which shows that there is a linear relationship between the elastic modulus of the pipe and the natural frequency of the structure. In engineering applications, if you want to avoid resonance by changing the stiffness of the structure, you can consider replacing the pipe, but you need to perform power calculations on the pipeline system to meet the stiffness requirements and avoid the length of the resonance pipe.

Material Poisson's ratio
As mentioned before, the steel used in the experimental pipeline system is 20# carbon steel with Poisson's ratio of 0.3. In this case, the numerical simulation has been carried out in the initial calculation example. Considering the general range of Poisson's ratio of carbon steel and the convenience of numerical comparison, the Poisson's ratio of the pipeline material in this numerical simulation is 0.28, 0.29, 0.31 and 0.32, respectively. The cloud diagram of simulation displacement distribution under Poisson's ratio of 0.28 is shown in Figure 15, the maximum displacement of the mesh under Poisson's ratio simulation of each material is shown in Table 5:  1 From the analysis of the results under the above charts, it can be seen that the maximum overall displacement is almost unchanged, and the Poisson's ratio of the material has a small effect on the vibration of the pipeline. The modal analysis found that the natural frequency and mode shape did not change much, and the influence of Poisson's ratio was limited.

Summary
(1) Different pipelines are affected differently by fluid-structure interaction. Branch pipelines or pipes with a small overall stiffness are more significant, and the performance of fluid-structure coupling will significantly increase the pipeline vibration. While main pipelines or pipes with large overall stiffness are relatively less affected by fluid-structure interaction.  (2) The medium pressure and the elastic modulus of the pipe have a greater impact on the natural frequency of the pipe and the fluid-solid coupling vibration, and the pressure is positively related to the vibration strength, the elastic modulus is negatively related to the vibration strength, the influence of the fluid solid coupling on the vibration of the pipe cannot be ignored under the condition of high medium pressure and low elastic modulus of the pipe.
(3) The medium density, dynamic fluid velocity, and Poisson's ratio of the pipe will only affect the natural frequency and fluid-structure coupling vibration of the pipeline under extreme operating conditions that are not very realistic, and generally have relatively small effects.